The United States and the United Kingdom have used standardized high-stakes testing as a measurement of students' cognitive level to determine success in the 21st century. Standardized tests have given teachers guidance to help them determine what to teach students and how to teach to the test. With such increased emphasis on high-stakes…

Although the importance of mathematical problem solving is now widely recognised, relatively little attention has been given to the conceptualisation of mathematical processes such as representing, analysing, interpreting and communicating. The construct of Mathematical Knowledge for Teaching (Hill, Ball & Schilling, 2008) is generally…

A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…

In this paper, we report on survey and focus group data relating to the activities and perceptions of learning with Web 2.0 technologies of students aged between 11 and 16 years in 27 UK secondary schools. The study confirms that these learners had high levels of access to Web 2.0 technologies and that Web 2.0 activities were prolific. However,…